Abstract
Historical churches have shown a dramatic vulnerability in several recent earthquakes, especially when they are adjacent to bell towers. Due to their great number and their societal relevance, low cost and nondestructive survey and investigation procedures are necessary for the seismic assessment. Accurate and fast geometric models can be obtained through digital photo-modeling, and they are the base for finite element models. These models can be updated through ambient vibration testing, which delivers a robust estimate of the fundamental period of the building especially in the case of cantilever-like bell towers. Elastic modulus and boundary conditions can be evaluated through numerical and physical comparison, provided that in situ sampling suggests a masonry density value. Then, compressive strength can be estimated, yielding a more robust seismic assessment. The proposed procedure is applied to the Cathedral of Matera, Southern Italy.
TopIntroduction
Historical and recent earthquakes showed the high vulnerability of unreinforced masonry churches, with Italian events of the last two decades involving several thousands of religious buildings (Lagomarsino & Podestà, 2004), and significant consequences even in the Christchurch, New Zealand, events (Marotta et al., 2015). Therefore, there is the need for low-cost, non-destructive technologies to gain an adequate knowledge of these structures, in order to assess the seismic risk of such extensive heritage. This task is further complicated because the earthquake performance of churches can be markedly affected by the interaction between the main body of the building and adjacent structures, such as the bell towers. The survey of bell towers can be hampered by their great height and the impossibility to access their external sides due to the presence of other constructions. Moreover, the interaction between adjacent structures of very different geometry can be difficult to model, and even the assumption of boundary conditions can be fraught with uncertainty (Gizzi et al., 2014). Additionally, the 2009 L’Aquila earthquake, central Italy, and the 2012 Emilia earthquake, northern Italy (Sorrentino et al., 2014a), just to mention the two most recent and relevant national events, showed that the interaction of the bell towers with adjacent structures can be crucial.
In this chapter the previous issues are discussed with reference to the Cathedral of Matera, southern Italy (Figure 1). As part of an ongoing restoration, and given the earthquake hazard of the region as well as the large gathering of people occurring at times in the building, a preliminary seismic assessment was needed, but both the available survey and the material properties knowledge were incomplete. Despite such start conditions budget was very limited, and the nature of the artifact excluded the resort to invasive testing. Hence, low-cost and non-destructive emerging technologies have been used to acquire an adequate knowledge of the church and perform quantitative assessment of the expected earthquake performance.
Figure 1. Location of Matera in Italy
TopBackground
Historically, direct methods have been used for the survey and analysis of architectural artifacts, however, tools and procedures for direct survey have often to confront the difficulty of not being able to physically reach all parts of large and geometrically complex architectures. In recent decades, increasingly efficient and technologically advanced instrumentation have become available. Moreover, analysis and interpretation of heritage elements is a painstaking activity, which requires a wide range of interdisciplinary subjects and competences, covering historical, survey, and structural issues. Innovative tools can simplify the collaboration between the involved people and enhance the outcomes of the documentation process of cultural heritage (Bianchini, 2012).
The dense stereo matching (DSM), or image based modeling, technologies are innovative techniques of survey that allow creating, from simple raster images, a three-dimensional point cloud. The scientific background of the procedure is the same of optical photogrammetry: analyzing two photos, shot from well separated locations, it is possible to get quantitative geometric information about a physical object and the surrounding environment (Docci & Maestri, 1994). However, optical photogrammetry is performed by specialized professionals, and the tools used are not always low-cost ones. The new technologies, on the other hand, open up enormous possibilities to collect, elaborate and share data much faster and automatically (Barazzetti et al., 2011).
The DSM technology originates in the theory of photogrammetry and makes it possible to draw three dimensional (3D) graphic models on the basis of photographs. This operation becomes comprehensible if one knows the relation between perspective and measurement.
Key Terms in this Chapter
Photo-Modeling: Method to obtain a realistic 3D model from photos. The object is reconstructed by projecting, in a 3D space, points and lines generated by image-matching algorithms, which allow the totally automated correlation of homologous points in different frames. The connection between pairs of frames is accomplished by dividing the frames in a grid of small squares. For each square in one of two images, the algorithm searches the one in the second image that has most similarities.
Ambient Vibration Measurement: Recording, evaluation and interpretation of the vibration behavior of a structure under ambient influences, i.e., without artificial excitation.
Modulus of Elasticity: Number that measures a material resistance to elastic (i.e., non-permanent) deformation when a force is applied to it. The elastic modulus of a material is defined as the slope of the stress–strain curve, of a specimen made of said material, in the elastic deformation region. A stiffer material has a higher elastic modulus. It is also called Young’s modulus.
3D Model: Communication tool for the understanding of a real object, based on a 3D representation in a virtual space. A figurative 3D model is purely informative, and identifies the geometry of the object and its components. A scientific purpose 3D model has a higher dimensional and formal correspondence with the real object, requiring highly precise survey data.
Amplitude Spectrum: Square root of a power spectrum. For a given signal (amplitude varying with time), the power spectrum gives a plot of the portion of a signal’s power (energy per unit time) falling within given frequency bins.
Fundamental Frequency of a Structure: The lowest frequency of vibration of a structure, where the frequency is the number of cycles of vibration of a mode shape carried out in the unit of time. A mode shape is the pattern of motion in which all parts of the system move harmonically with same frequency and deflected shape.
Finite Element Method: Numerical method for finding approximate solutions to partial differential equations. The original problem domain is subdivided into smaller and simpler parts, called finite elements, and variational techniques are used to minimize an associated error function.
Viscous Damping Ratio: A dimensionless measure describing how oscillations in a system decay after a disturbance: the higher the ratio the faster the decay. Damping is considered viscous if proportional to velocity.
3d Survey: Process that involves the critical interpretation of a real object and delivers its representation through 2D and 3D graphic models at an appropriate scale of representation. The procedure can be carried out with non contact techniques, such as 3D laser scanning, characterized by high precision, or photo-modeling, characterized by quick acquisition and elaboration.